Concept for determining a measure for a distortion change in a synthesized view due to depth map modifications

ABSTRACT

An apparatus for determining a measure for a distortion change of a first view synthesized from a second view, caused by a modification of a depth map of the second view from a first state to a second state, is configured—starting from a current synthesis state of the first view corresponding to a synthesis from the second view having the depth map modified to the second state in an already processed portion of the depth map and having the depth map unmodified at the first state in a yet to be processed portion of the depth map—to compute a possible successor synthesis state corresponding to a synthesis of the first view from the second view having the depth map modified to the second state in an already processed portion plus a currently processed portion and having the depth map unmodified at the first state in the yet to be processed portion without the currently processed portion; and to determine a distortion change of a distortion of the current synthesis state of the first view relative to an undistorted version of the first view to a distortion of the possible successor synthesis state of the first view relative to the undistorted version of the first view.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of copending InternationalApplication No. PCT/EP2012/072128, filed Nov. 8, 2012, which isincorporated herein by reference in its entirety, and additionallyclaims priority from U.S. Application No. 61/558,656, filed Nov. 11,2011, which is also incorporated herein by reference in its entirety.

The present invention is concerned with determining a measure for adistortion change in a synthesized view due to depth map modificationsin the reference view such as occurring in depth map encoding, depthfiltering, a depth estimation or the like.

BACKGROUND OF THE INVENTION

For the representation of stereo and 3D-video several methods have beenproposed [1]. One of the methods for 3D video is the Multi-View plusDepth (MVD) format. The MVD-format stores the scene information as twoor multiple texture views depicting the 3D-scene from differentperspectives. Additionally the scene geometry is represented by a fulldense depth map per texture view. The MVD format supports the generationadditional texture views located in between the provided views by depthimage based rendering (DIBR). For this the samples of the views'textures are warped using disparities obtained from their depth map.

Modern auto stereoscopic displays provide a high view density with eightto 28 or even more views. However, recording of a 3D scene in a reallive scenario can only be accomplished with a small number of cameras.Thus, the possibility to generate intermediate views as provided by theMVD format is a feature that may be used for a 3D video system. Moreoverthe usage of depth maps and view interpolation provide advantagesregarding the transmission of 3D-video. Depth maps can be coded at ahighly reduced rate compared to a video view and may use less bandwidth.

Compared to multi-view video, the generation and transmission of depthbased video involves additional processing steps at the sender andreceiver side. In particular, depth modifications due to, for example,lossy compression, results in distortions of the depth map itself.However, most importantly is the distortion of a synthesized viewsynthesized from the view of the modified depth map, and accordingly,for performing a rate/distortion optimization correctly, the distortioncaused by the modification of depth map would have to be somehow takeninto account when optimizing. However, until now, such determination isnot performed in an exact manner due to the overhead associatedtherewith.

SUMMARY

According to an embodiment, an apparatus for determining a measure for adistortion change of a first view synthesized from a second view, causedby a modification of a depth map of the second view from a first stateto a second state, may be configured to perform the steps of: startingfrom a current synthesis state of the first view corresponding to asynthesis from the second view having the depth map modified to thesecond state in an already processed portion of the depth map and havingthe depth map unmodified at the first state in a yet to be processedportion of the depth map, computing a possible successor synthesis statecorresponding to a synthesis of the first view from the second viewhaving the depth map modified to the second state in an alreadyprocessed portion plus a currently processed portion and having thedepth map unmodified at the first state in the yet to be processedportion without the currently processed portion; determining adistortion change of a distortion of the current synthesis state of thefirst view relative to an undistorted version of the first view to adistortion of the possible successor synthesis state of the first viewrelative to the undistorted version of the first view.

According to another embodiment, a method for determining a measure fora distortion change of a first view synthesized from a second view,caused by a modification of a depth map of the second view from a firststate to a second state, may have the steps of: starting from a currentsynthesis state of the first view corresponding to a synthesis from thesecond view having the depth map modified to the second state in analready processed portion of the depth map and having the depth mapunmodified at the first state in an yet to be processed portion of thedepth map, computing a possible successor synthesis state correspondingto a synthesis of the first view from the second view having the depthmap modified to the second state in an already processed portion plus acurrently processed portion and having the depth map unmodified at thefirst state in the yet to be processed portion without the currentlyprocessed portion; determining a distortion change of a distortion ofthe current synthesis state of the first view relative to an undistortedversion of the first view to a distortion of the possible successorsynthesis state of the first view relative to the undistorted version ofthe first view.

According to another embodiment, a computer program may have a programcode for performing, when running on a computer, a method according toclaim 15.

In particular, in accordance with embodiments of the present invention,an apparatus for determining a measure for a distortion change of afirst view synthesized from a second view, caused by a modification of adepth map of the second view from a first state to a second state isconfigured—starting from a current synthesis state (s′_(T)) of the firstview corresponding to a synthesis from the second view (s_(T)) havingthe depth map modified to the second state ({tilde over (s)}_(D)) in analready processed portion (B₁∪B₂ . . . ∪B_(N-1)) of the depth map andhaving the depth map unmodified at the first state (s_(D)) in a yet tobe processed portion (I\(B₁∪B₂ . . . ∪B_(N-1))) of the depth map—tocompute a possible successor synthesis state corresponding to asynthesis of the first view from the second view (s_(T)) having thedepth map modified to the second state ({tilde over (s)}_(D)) in analready processed portion (B₁∪B₂ . . . ∪B_(N-1)) plus a currentlyprocessed portion (B_(N)) and having the depth map unmodified at thefirst state (s_(D)) in the yet to be processed portion (I\(B₁∪B₂ . . .∪B_(N-1))) without the currently processed portion; and to determine adistortion change (ΔD_(B) _(N) ) of a distortion of the currentsynthesis state (s′_(T)) of the first view relative to an undistortedversion of the first view to a distortion of the possible successorsynthesis state (s′_(T)) of the first view relative to the undistortedversion of the first view.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will be detailed subsequentlyreferring to the appended drawings, in which:

FIG. 1 shows processing steps to generate and transmit a video plusdepth based 3D video format as a possible application scenario whereembodiments of the present invention may be employed;

FIG. 2 shows a rendering process according to an embodiment, modeled asstate machine;

FIG. 3 shows an example for the dependencies between input, intermediateand output signals of the rendering or error calculation step;

FIG. 4 shows basic steps of extrapolation of view s′_(T) from one view(s_(T), s_(D));

FIG. 5 Basic steps of interpolation of intermediate view s′_(T) from aleft view (s_(T,l), s_(D,l)) and a right view (s_(T,r), s_(D,r));

FIG. 6 shows a flow chart of one iteration of the warping and instantinterpolation and hole filling process;

FIG. 7 shows scenarios for rendering the shifted interval related to theflow chart in FIG. 6;

FIG. 8 shows a flow chart of for the recovery of the auxiliary variablex′_(MinOccl);

FIG. 9 shows an example for recovery of the auxiliary variablex′_(MinOccl);

FIG. 10 shows an overview of intervals in the synthesized view affectedby the change of the depth map;

FIG. 11 shows a flow chart of the warping, interpolation and instanthole filling process for changed depth data;

FIG. 12 shows a flow chart of the warping and instant hole fillingprocess for data left to the changed depth data;

FIG. 13 shows a distortion computation for three input views and twofour synthesized views;

FIG. 14 shows the modifications to a encoder to integrate the presentconcept

FIG. 15 shows different possibilities to generate the reference views′_(Ref) and the view to test s′_(T); and

FIG. 16 shows different possibilities to generate the reference views′_(Ref) and the view to test s′_(T).

DETAILED DESCRIPTION OF THE INVENTION

As described above, compared to multi-view video, the generation andtransmission of depth based video involves additional processing stepsat the sender and receiver side. These steps are shown in the top box ofFIG. 1.

Thus, FIG. 1 shows a possible environment into which the embodiments ofthe present invention outlined further below may be advantageouslyemployed. In particular, FIG. 1 shows a multi-view coding environmentwhere a pair of encoder 10 and decoder 12 is responsible forcoding/decoding the texture sample arrays of the different views of amulti-view signal, while a pair of encoder 14 and decoder 16 isresponsible for encoding and decoding the associated depth/disparitymaps associated with each view. The encoding of encoders 10 and 14 maybe implemented so as to achieve lossy compression such as by way ofblock-based hybrid coding. The decoders 12 and 16 reconstruct thereconstructible version of texture and depth/disparity maps,respectively. Within the encoder side, a depth estimator 18 may beprovided in order to estimate the depth/disparity map associated witheach picture/texture map of the views, with depth filter 20 beingconfigured to remove estimation outliers from the estimateddepth/disparity maps. In particular, the depth estimator 18 associates,for example, a depth/disparity value with each texture sample of theviews. In the following description, the term “depth map” shallencompass both versions, the association of a disparity value or anassociation of a depth value to the texture samples as depth anddisparity are easily convertible to each other. The lossy nature of thecompression performed by encoder 14 causes modifications in the depthmaps resulting from depth estimator 18 and depth filter 20 and assumingthat the output of modules 18 and 20 was correct, these modificationscause, naturally, quality degradations in views synthesizable from thebase views using these modified depth maps, namely by warping the baseviews using the modified depth maps into other views such asintermediate views or the like. Conventionally, i.e. in conventionalcoding environments 8, as a measure for these degradations, a measure ofthe variation of the depth map itself is used. However, the depth mapvariation is not visible to the user, and accordingly such a depth mapvariation measure is not a good measure for the distortion in thesynthesized views caused by the depth map modifications caused byencoder 14. Accordingly, a renderer model 24 configured to determine ameasure for a distortion change of a synthesized view caused by suchdepth map modification is introduced into the chain of depth mapestimator 18 down to a renderer 22 which renders the synthesized viewsbased on the reconstructed texture and reconstructed depth map. Therenderer 24 is connected with renderer 22 so as to steer or control theoptimization of the parameter settings within each of, or at least apart of, modules 18, 20 and 14. To this end, the renderer model 24compares the synthesized views resulting from the depth mapmodifications as obtained from renderer 22 either with reference views,which might be provided from elsewhere, or with the synthesized viewsresulting from synthesizing using the originally estimated or originallyestimated and filtered depth maps.

Thus, in FIG. 1 each of modules 8 (as far as the encoding side isconcerned), 18, 20 and 14 may act as a depth modifier performing trialsof different modifications of a depth map, and the renderer model 24along with renderer 16 form an apparatus for determining a measure for adistortion change in accordance with the below outlined procedure. Theyparticipate in searching the best trial in terms of a rate/distortionoptimization sense or some other cost function optimization using a costfunction depending on a distortion of the synthesized view.

The depth estimation step may be performed if depth data has not beendirectly recorded with depth cameras. Disparity maps corresponding tothe views' textures are obtained carrying out stereo or multi-viewmatching. After depth estimation an optional depth filtering can beapplied, to reduce irrelevant signal parts and noise from the depthmaps. Subsequently the depth data is encoded, transmitted and decoded.At the receiver side the rendering of the intermediate views has to becarried out.

Conventionally depth estimation, filtering and encoding are conductedindependently from the rendering process. However, an improvement in allthree steps can be achieved by regarding the rendering process and thesynthesized view distortion, as depicted in the bottom box in FIG. 1.Therefore, an embodiment for synthesized view distortion computation ispresented hereinafter. Approximations for the synthesized viewdistortions have been analyzed and used in encoding in [2], [3] and [4].However, in contrast to these approaches, the embodiment outlined belowforms a renderer that provides not an approximation but the correctsynthesized view distortion change assuming a simple renderer. Therenderer determines a measure for a distortion change of a first viewsynthesized from a second view, caused by a modification of a depth mapof the second view. The renderer supports the basic functionalitiesshared by most rendering approaches, like sub pixel accurate warping,hole filling and view blending. To calculate the synthesized viewdistortion depending on a distortion of the depth signal the renderer ismodeled as a state machine, called renderer model in the following. Therenderer model is designed for fast re-rendering of parts of thesynthesized view to obtain the synthesized view distortion.

In following subsections 1.1.1 and 1.1.2 the basic idea of the rendererand related works for comparison reasons are discussed in detail.Subsequently the renderer considered for distortion computation ispresented in section 1.2. How this renderer can be extended to therenderer model is described in section 1.3. Finally the new features ofthe renderer model are summarized in section 1.4.

1.1.1 Basic Idea

The geometry information given by depth data are exploited in therendering process only. Hence distortions of depth data lead indirectlyto subjective perceivable synthesized view distortions. The depth mapitself is not visible for a viewer. Applications processing depth data,like depth estimation, depth filtering or depth coding can be improvedby regarding this property. Therefore decisions carried out within thedepth processing algorithm can be modified to be based on thesynthesized view distortion instead of the depth distortion.

Assuming the extrapolation of a the synthesized texture s′_(T) therendering process can be modeled as function of an input depth map s_(D)and an input texture s_(T)

s′ _(T)(x′,y′)=f _(H) [s _(T)(x,y),s _(D)(x,y)]  (1)

with (′) marking signals in the synthesized domain. Given the texture{tilde over (s)}′_(T) synthesized from distorted depth data {tilde over(s)}_(D), the synthesized view distortion D can be defined as the sum ofsquared differences to a reference view s′_(Ref) as shown in eq. (2).

$\begin{matrix}{D = {{f_{D}\left( {{\overset{\sim}{s}}_{T}^{\prime},s_{Ref}^{\prime}} \right)} = {\sum\limits_{x^{\prime} = 1}^{w}{\sum\limits_{y = 1}^{h}\left\lbrack {{{\overset{\sim}{s}}_{T}^{\prime}\left( {x^{\prime},y^{\prime}} \right)} - {s_{Ref}^{\prime}\left( {x^{\prime},y^{\prime}} \right)}} \right\rbrack^{2}}}}} & (2)\end{matrix}$

with w and h denoting the width and height of the view. Depending on theuse case s′_(Ref) can be an original texture at the position of thesynthesized view or the texture s′_(T), synthesized from original videodata s_(T) and depth data s_(D). Note that if an original texture isused, the initial synthesized view distortion D₀ related to the originaldepth map might not be equal to zero.

Combining eq. (1) and eq. (2) shows that D is a function of the inputtexture s_(T), the distorted input depth {tilde over (s)}_(D) and thereference texture s′_(Ref). For simplification a constant s_(T) and aconstant s′_(Ref) is assumed in the following. Thus, the synthesizedview distortion D is expressed as function of the input depth map only.

D=f _(D)({tilde over (s)} _(D))  (3)

D is the total distortion of the whole view related to the completedistorted depth map {tilde over (s)}_(D). However, processing of depthdata is commonly applied block wise. Hence, a distortion functionsimilar to eq. (2) providing a global distortion related to completedistorted depth map {tilde over (s)}_(D) is not useful. Commonlydistortion functions f applied in depth processing have two properties.First of all only the distortion D_(B) caused by the change of the depthwithin a block B of the depth map s_(D) is of interest. Therefore frelates the distorted depth data within block B to the distortion D_(B)

D _(B) =f[{tilde over (s)} _(D)(B)]  (4)

with {tilde over (s)}_(D) (B) denoting the part of {tilde over(s)}_(D)(x,y) with (x,y)εB.

Secondly, f should satisfy the superposition property. It should bepossible to obtain the distortion caused by a change of the depth datain different blocks independently. The sum of this independentlycomputed distortions should be equal to the distortion obtained for theblock merged of all blocks. For e.g. a distortion of the depth data oftwo blocks B₁ and B₂

D _(B) ₁ _(∪B) ₂ =f[{tilde over (s)} _(D)(B ₁ ∪B ₂)]

D_(B) ₁ +D _(B) ₂ =f[{tilde over (s)} _(D)(B ₁)]+f[{tilde over (s)}_(D)(B ₂)]  (5)

should be true. Here, D_(B) ₁ _(∪B) ₂ denotes the distortion related tothe merged block B₁∪B₂.

Some depth coding ([4], [3]) approaches use a distortion functionoffering these two properties. However, these approaches only provide anapproximation of the synthesized view distortion. In the following it isshown that these two properties cannot be fulfilled by a distortionfunction providing a correct synthesized distortion and not anapproximation. Moreover it is presented how a distortion function withsimilar properties suitable for depth processing can be constructed.

To get a further insight, how the correct synthesized view distortion iscalculated and how it can be related to parts of the input depth map adistorted depth map consisting of two blocks B₁ and B₂ is analyzed. Eq.(2) shows that the correct synthesized view distortion is a function ofthe synthesized view s′_(T). The synthesized view again depends throughthe rendering on all samples B₁∪B₂=1 of depth map in a nonlinear way ascan be seen in eq. (1). Due to occlusion and hole filling a change ofthe depth data within a block cannot be related to synthesized viewdistortion without regarding depth data outside the block. It is forexample possible, that positions in the synthesized view related to B₁are occluded by samples shifted from positions of B₂. Or the change ofthe depth data within B₁ uncovers samples shifted from block B₂. Samplesbelonging to B₁ and B₂ can interact in the synthesized view, producing amutual distortion term D_(B) ₁ _(∩B) ₂ , that cannot be related to B₁ orB₂ solely. Hence, the total synthesized view distortion can formally bedefined as

$\begin{matrix}\begin{matrix}{D_{B_{1}\bigcup B_{2}} = {f_{D}\left\lbrack {{\overset{\sim}{s}}_{D}\left( {B_{1}\bigcup B_{2}} \right)} \right\rbrack}} \\{= {D_{B_{1}} + D_{B_{2}} + D_{B_{1}\bigcap B_{2}} + D_{0}}} \\{\neq {D_{B_{1}} + D_{B_{2}}}}\end{matrix} & (6)\end{matrix}$

with D₀ denoting the initial distortion and D_(B) ₁ and D_(B) ₂ denotingdistortion terms solely related to B₁ or B₂. Eq. (6) shows that thedistortion D_(B) ₁ _(∪B) ₂ related to the merged blocks B₁ and B₂ cannotbe derived by summing up independently obtained distortion D_(B) ₁ andD_(B) ₂ . A superposition as shown in eq. (5) is not possible.

However, as stated above, the superposition property may be used formost applications. To resolve this issue, a distortion functionsatisfying the superposition property can by constructed by consideringa block related global synthesized view distortion change ΔD. Assuming asequential processing of the blocks of the depth map the distortionchange of the first block can be defined as

ΔD _(B) ₁ =f _(D) [{{tilde over (s)} _(D)(B ₁),s _(D)(B ₂)}]−D ₀  (7)

with {{tilde over (s)}_(D)(B₁), s_(D)(B₂)} denoting the image formedfrom {tilde over (s)}_(D)(x,y) for (x,y)εB₁ and s_(D)(x,y) for (x,y)εB₂.Hence the distortion change ΔD_(B) related to B₁ is the globaldistortion of the texture rendered from the depth map consisting ofdistorted depth data within block B₁ and original depth data outside ofB₁ minus the initial distortion D₀. Similarly the distortion changeΔD_(B) ₂ for the second block is

$\begin{matrix}\begin{matrix}{{\Delta \; D_{B_{2}}} = {{f_{D}\left\lbrack {{\overset{\sim}{s}}_{D}\left( {B_{1}\bigcup B_{2}} \right)} \right\rbrack} - {f_{D}\left\lbrack \left\{ {{{\overset{\sim}{s}}_{D}\left( B_{1} \right)},{s_{D}\left( B_{2} \right)}} \right\} \right\rbrack}}} \\{= {{f_{D}\left\lbrack {{\overset{\sim}{s}}_{D}\left( {B_{1}\bigcup B_{2}} \right)} \right\rbrack} - {\Delta \; D_{B_{1}}} - D_{0}}} \\{= {D_{B_{1}\bigcup B_{2}} - {\Delta \; D_{B_{1}}} - D_{0}}} \\{= {{\Delta \; D_{B_{1}\bigcup B_{2}}} - {\Delta \; D_{B_{1}}}}}\end{matrix} & (8)\end{matrix}$

It can be seen from eq. (8) that using the distortion change asdistortion function satisfies the superposition property. Generalizingeq. (8) leads to a distortion change for block B_(N) of

$\begin{matrix}\begin{matrix}{{\Delta \; D_{B_{N}}} = {{f_{D}\left\lbrack \left\{ {{{\hat{s}}_{D}\left( {\bigcup\limits_{i = 1}^{N}B_{i}} \right)},{s_{D}\left( {I\backslash {\bigcup\limits_{i = 1}^{N}B_{i}}} \right)}} \right\} \right\rbrack} -}} \\{{f_{D}\left\lbrack \left\{ {{{\overset{\sim}{s}}_{D}\left( {\bigcup\limits_{i = 1}^{N - 1}B_{i}} \right)},{s_{D}\left( {I\backslash {\bigcup\limits_{i = 1}^{N - 1}B_{i}}} \right)}} \right\} \right\rbrack}} \\{= {D_{B_{1}\bigcup{B_{2}\mspace{14mu} \ldots}\mspace{14mu}\bigcup B_{N}} - D_{B_{1}\bigcup{B_{2}\mspace{14mu} \ldots}\mspace{14mu}\bigcup B_{N - 1}}}} \\{= {{\Delta \; D_{B_{1}\bigcup{B_{2}\mspace{14mu} \ldots}\mspace{14mu}\bigcup B_{N}}} - {\sum\limits_{i = 1}^{N - 1}{\Delta \; D_{B_{i}}}}}}\end{matrix} & (9)\end{matrix}$

with I\B denoting all samples with (x,y)B.

The global distortion change defined by eq. (9) provides a block relateddistortion metric with superposition property. However, due to therecursive definition of ΔD_(B), it also depends on the view distortioncurrently realized in other blocks of input depth data. Hence, the valueof ΔD_(B) _(N) also depends on the processing order of the blocks of theinput depth. This dependency is a minor disadvantage that is shared byother algorithm like e.g. entropy coding or intra coding.

As can be seen from eq. (9), the computation of the distortion changeΔD_(B) _(N) involves rendering a synthesized texture using the depthdata of the previous distortion computation modified with the new dataof B_(N) block. However, the complete rendering of a whole view iscomputational too complex to be feasible. To overcome this problem amethod is presented that only re-renders parts of the synthesized view,that are affected by the change of the depth data in the block B_(N).Therefore intermediate data of the rendering process are stored and usedtogether with the new depth data for re-rendering. FIG. 2 shows how thisre-rendering method can be modeled as state machine. In the followingthis state machine is called renderer model.

Accordingly, a measure for a distortion change of a first viewsynthesized from a second view, caused by a modification of a depth mapof the second view from a first state to a second state may determinedeffectively if, starting from a current synthesis state of the firstview corresponding to a synthesis from the second view having the depthmap modified to the second state ({tilde over (s)}_(D)) in an alreadyprocessed portion B₁∪B₂ . . . ∪B_(N-1) of the depth map and having thedepth map unmodified at the first state SD in a yet to be processedportion I\(B₁∪B₂ . . . ∪B_(N-1)) of the depth map, a possible successorsynthesis state corresponding to a synthesis of the first view from thesecond view having the depth map modified to the second state {tildeover (s)}_(D) in an already processed portion (B₁∪B₂ . . . ∪B_(N-1))plus a currently processed portion B_(N) and having the depth mapunmodified at the first state (s_(D)) in the yet to be processed portionI\(B₁∪B₂ . . . ∪B_(N-1)) without the currently processed portion iscomputed, with then determining a distortion change ΔD_(B) _(N) of adistortion of the current synthesis state of the first view relative toan undistorted version of the first view to a distortion of the possiblesuccessor synthesis state (s′_(T)) of the first view relative to theundistorted version of the first view at 32. The state is, however, notchanged until the modification of the depth map has been finallydetermined. The latter change of the renderer's state, i.e. the update,is performed at 30 with the result of step 30 being the new, updatedstate 31. The flow chart of FIG. 2 is passed for each currentlyprocessed portion until the final selection of the modification of thedepth map therein, with then passing the flow chart for the subsequentto be processed portion. This is, what the renderer 24 described furtherbelow does.

In particular, the depth map modification may have been caused by any ofmodules 18, 20 and 14, and the currently processed portion maycorrespond to, for example, the currently inspected block of theblock-based hybrid encoding of encoder 14, or some other currentlyprocessed portion of depth estimator 18 and depth filter 20,respectively. In that case, the already processed portion would be thesum of already passed blocks of encoder 14 or the already passedportions of estimator 18 and filter 20, respectively, while theremaining yet to be processed portions would correspond to blocks withinthe currently coded depth map not yet passed by encoder 14 or depth mapestimator 18 and depth filter 20, respectively.

The renderer model is defined by its possible inputs and outputs, therenderer's state 31, a state transition function 30 and an outputfunction 32. The input to the renderer model consists of the positionand size of a depth block to change, i.e. the currently processedportion, and the changed depth data itself. Moreover an indication isgiven within an input, determining if a state transition should becarried out or if the distortion change should be given as output, i.e.as to whether the depth map modification is finally selected so thatstate 31 may be changed according to the final selection. The set of thestates comprises all possible depth maps, combined with all possiblestates of the intermediate variables used for re-rendering. If the wishfor a state transition is signalized in the input, i.e. the finalselection of depth modification has been made, the state transitionfunction 30 performs the re-rendering of the block of changed depth datautilizing the current renderer state from the feedback loop leading fromthe state's 31 output to the input of function 30, and an empty outputis given. Otherwise the output function 32 computes the distortionchange, using the input data and the current state 31. The result isgiven as output and the render model stays in the same state. Thepossibility to obtain the synthesized distortion change without alteringthe renderer's state 31 is provided to allow a fast evaluation ofmultiple different depth changes.

So far only the extrapolation of a view from one texture and one depthmap has been regarded as given in eq. (1). However, view synthesize isconventionally carried out by using two input textures with associateddepth maps. For view interpolation one view is extrapolated from theleft and one view is extrapolated from the right. Subsequently bothviews are blended to obtain the final rendered view. Thus, thedistortion depends on two depth maps as given by

D=f _(D)({tilde over (s)} _(D,l) ,{tilde over (s)} _(D,r))  (10)

with {tilde over (s)}_(D,l) denoting the left depth map and {tilde over(s)}_(D,r) denoting the right depth map. To compute D for viewinterpolation, the principle of assuming original depth data in parts ofdepth maps that have not been processed as done in eq. (9) can easilyextended to two views. The formally defined renderer model as shown inFIG. 2 remains unchanged, except that the input additionally signalizeswhich of the two depth maps is altered. This allows the computation ofthe synthesized view distortion for arbitrary changes in both depthmaps.

So far the renderer model has only been presented as formally definedstate machine. In the following an overview of the basics ideas of thealgorithm realizing the renderer model is given. Main objective of thealgorithm is a computational low complex error calculation or statetransition, hence a low complex re-rendering of parts of the synthesizedview, that are affected by a depth change in one of the input depthmaps.

As described above conventional view synthesis consists of multiplesteps as e.g. warping of the input samples, interpolation at sub pixelpositions, blending with a second view obtained similarly and holefilling. Typically these steps are realized as independent algorithmsthat are applied successively using the results of the previous step.However, to enable fast re-rendering of only parts of the synthesizedview, the present concept integrates all steps to a single algorithmthat can be applied pixel wise to the input depth map.

How this is done is shown in the example give in FIG. 3. Rendering isapplied row wise in a processing direction 54, hence all depictedsignals represent one row of input, intermediate or output data. Thesingle signals are from bottom to top: the left input texture s_(T,l),i.e. the texture samples 49 of currently processed portion/block, forexample, a x′−s_(Disp,l) chart, i.e. the rendered texture samples 50 atsub-pa resolution, the texture synthesized from left s′_(T,l), thetexture synthesized from right s′_(T,r), the blended texture s′_(T),i.e. texture 52 as it would be obtained by a decoding side renderer22—with or without blending and using two views—and the referencetexture s′_(Ref), i.e. the texture 58 as it would have been obtained byrenderer 22 leaving the depth map unchanged, for example. The arrowsdenote the relationship between the single samples or sample positionsof the signals. Dots shown in the x′−s_(Disp,l) represent samples fromthe input view. Their horizontal position is equal to their position x′in the synthesized view. The vertical position shows their disparities.Since the depth is monotonically decreasing with the disparity, thetopmost samples in the chart are the samples closest to the camera.Hence, it can be seen from the x′−s_(Disp,l) chart which samples areoccluded in the synthesized view.

Whereas a conventional view synthesis approach would carry out thesingle steps depicted from bottom to top for all samples in theintervals (a) to (g), the present concept supports interval wiseprocessing. Hence, all steps are firstly conducted for interval (a)before continuing with interval (b). This approach yields twoadvantages. Firstly, re-rendering and error calculation can be carriedout by iterating only one time over the input samples depth samples.Secondly, if only the view synthesis distortion should be calculatedthere is no need to store intermediate results.

To point out the key features of the approach re-rendering of some ofthe intervals shown in FIG. 3 is discussed in the following. The widthsof the intervals in the input view are equal to the sampling distance.However, as can be seen in x′−s_(Disp,l) the interval width can bestretched or compressed in the synthesized view.

For interval (a) first the left and the right boundary samples areshifted in the warping process 40, it can be seen from the x′−s_(Disp,l)chart, that the shifted interval is not occluded. However, the left andright boundary samples have not been warped to full sample positions inthe synthesized view. Hence, an interpolation 42 at the full sampleposition located between the two shifted boundary samples is carriedout. To speed up this interpolation, the present concept maps a samplefrom an up-sampled version of the input texture to the interpolationposition in the synthesized view s′_(T,l). The exact position in theup-sampled view is derived from the distance of the interpolationposition to the interval boundaries. After the interpolated sample valuehas been obtained, blending 44 with the sample at the same position ins′_(T,r) is directly carried out to obtain the synthesized sample ins′_(T). If the renderer model shall carry out a state transition, allintermediate results are stored and processing is for interval (a) isfinished here. Otherwise, if the synthesized view distortion should beobtained only, intermediate results are not stored, but the algorithmcontinues with comparing the synthesized sample to the output view inerror calculation step 46 which is part of calculation 32, resulting inthe distortion D_(a).

The width of the warped interval (b) is very large, hence a disocclusioncan be assumed in the synthesized view. The two rightmost samples atinteger positions in the shifted interval may be filled by backgroundextrapolation or some other hold filling 48. The leftmost sample isclose to the left interval border and it is assumed that it belongs tothe foreground. Note, that these sample position might later beoverwritten in the blending process 46, if the s′_(T), has nodisocclusions at the same positions.

Interval (f) is entirely occluded 56 in the synthesized view. This isdetected by continuously memorizing the most left interval end 60 amongthe intervals processed so far and checking as to whether the currentinterval, here (f) lies to the right therefrom. Hence no furtherrendering or error calculation has to be carried out. As can be seenfrom the x′−s_(Disp,l) chart the information that interval (f) isocclude can be derived from the positions of the interval boundaries,hence no complex z-buffering is required. To easily derive whether othersamples left to interval (f) are occluded the rendering process storesthe shifted position of the front-most interval boundary of interval(f). This stored value can then be utilized for interval (e), todetermine which parts of the interval are occluded.

To obtain the synthesized view distortion change related to the changeof the depth map the single distortions D_(a)-D_(h) related to thechanged intervals a-h in the synthesized view are summed up. Moreover,and that is actually not depicted in FIG. 3, the old per-sampledistortions of the changed interval are subtracted. Another aspect to beregarded is that in some cases not only the intervals related to thechanged depth values are re-rendered, but some neighboring intervals aswell. Reason for this is that neighbor intervals that are occludedbefore a depth change become visible after the depth change. Theproposed algorithm detects such uncovering and continues rendering,until the complete changed interval in the synthesized view is updated.

Thus, in FIG. 3 the warping step 40 may be considered as the computationof a possible successor synthesis state determined by the warpedpositions 50 indicated with circles in FIG. 3. The possible successorsynthesis state is, however, also determined by the result of steps 44,42 and 48 leading to the synthesized texture samples s′_(T). The errorcalculation 46 summing over the single distortions D_(a)-D_(h) alongwith the not depicted, but above mentioned subtraction of the old errorrepresents the calculation of the distortion change 32 in FIG. 2. If thepossible successor synthesis state thus determined corresponds to thefinally selected modified depth map, then the resulting warped sampleposition 50 along with s′_(T) represent the new synthesis state for thenext to be processed portion of the depth map, and this state transitionis performed by function 30.

In this section it was shown how a distortion function can be definedproviding a block related synthesized view distortion change. Moreover astate machine modeling the rendering process and an algorithm realizingthis state machine have been presented. A detailed description of themodeled rendering process can be found in the section 1.2. Section 1.3discusses how this rendering process can be extended to the renderermodel.

1.1.2 Related Works

The usage of the synthesized view distortion in depth coding has beeninvestigated by Kim et. al [4], [3] and Oh et al. [2]. In [4] anapproximation of the synthesized view distortion is derived fromcomparing a texture block of the input view to a block consisting ofsamples shifted by the geometry error derived from the depth error.Furthermore an autoregressive model is provided that reduces thecomputational complexity of the approach. In [3] the synthesized viewdistortion is assumed to be proportional to the disparity error. Thefactor between synthesized view distortion and disparity error isderived globally or locally using a least square fit. The modelpresented in [2] utilizes a distortion function based on the localtexture characteristics and the depth error in a multiplicative way.Moreover occlusion handling is regarded. However, none of the methodsprovides the correct view synthesis distortion or regards the blendingprocess, as done by the renderer model.

1.2 RENDERING ALGORITHM

Unlike other methods that estimate the distortion in synthesized viewscaused by a distortion of depth data the present concept computes theexact distortion change of the synthesized view using a simple renderingalgorithm. Hence, effects of occlusions, disocclusions, blending andhole filling can be regarded. The applied rendering algorithm isdescribed in this section. The algorithm is designed in a way that itcan be easily extended to the renderer model. How this is done isexplained in section 1.3.

The renderer allows view interpolation and view extrapolation. For theview interpolation case the input views need to be rectified. For viewextrapolation and view interpolation the synthesized output texture ofthe renderer is rectified to the input view or views as well. Hence,apart from chroma up- and down-sampling steps, each row of the view tobe synthesized can be processed independently.

For view extrapolation the synthesized texture s′_(T) is rendered froman input texture s_(T) and a corresponding input depth map s_(D). Hence,the rendering process can be described as:

s′ _(T) =f _(B)(s _(T) ,s _(D))  (11)

Signals in the warped domain are marked with an apostrophe (') in thefollowing. The single steps of the view extrapolation are depicted inFIG. 4. First the input texture s_(T) is up-sampled. Subsequently theup-sampled texture is warped to position of the view to extrapolate. Thewarping process is combined with interpolation and hole filling. Notethat with interpolation, the interpolation at full sample positions inthe synthesized view is meant here. If a chroma channel of the inputtexture with a lower resolution than the luma channel should berendered, its sampling rate is increased to the luma sampling rate inthe up-sampling step. After warping, interpolation and hole filling thechroma component can be optionally reduced to its original samplingrate.

When conducting view interpolation the synthesized texture s′_(T) isrendered from a left and right input textures s_(T,l) and s_(T,r), aswell as corresponding left and right depth maps s_(D,l) and s_(d,r):

s′ _(T) =f _(R)(s _(T,l) ,s _(T,r) ,s _(D,l) ,s _(D,r))  (12)

In the following symbols denoting signals of the left or right viewcontain l or r.

The view interpolation process is depicted in FIG. 5. It can be seenthat view interpolation is carried out by first extrapolating a textures′_(T,l) from the left view and a texture s′_(T,r) from the right viewto the position of the view to be synthesized. These two textures arecombined by blending to create the synthesized output texture s′_(T).For blending additional signals are needed that are produced in thewarping, interpolation and hole filling process as well. These signalsare the warped depth maps s′_(D,l) and s′_(D,r) and the filled mapss′_(F,l) and s′_(F,r).

Note that also depicted as independent step, blending is carried outinstantly in the warping, interpolation and hole filling process toreduce computational complexity. This means if e.g. s′_(T,l)(x) hasalready been rendered, s′_(T)(x) is can directly be computed in theinterpolating and hole filling process of the right view afters′_(T,r)(x) has been obtained. In the next sections the processing stepsused for rendering are discussed in detail.

1.2.1 Up-Sampling

Up-sampling is conducted to enable sub-pixel accurate warping. The lumacomponent of the input texture signal s_(T) is up-sampled by a factor offour in horizontal direction, using the same sampling filters as in theHM software version 3.0 described in [5] which serves as an example fora typical hybrid block-based multi-view encoder including depth mapencoding, here a HEVC codec with multi-view coding capability includingdepth map encoding. [5] is incorporated herein by reference for detailsregarding the encoding and optimization procedure. Interpolation filtersare given in table 1. The up-sampled signal is denoted as ŝ_(T).

TABLE 1 Luma upsampling filter from HM software version 3.0 [5] PositionCf. 0 Cf. 1 Cf. 2 Cf. 3 Cf. 4 Cf. 5 Cf. 6 Cf. 7 Div 1/4 −1 4 −10 57 19−7 3 −1 64 2/4 −1 4 −11 40 40 −11 4 −1 64 3/4 −1 3 −7 19 57 −10 4 −1 64

To avoid down-sampling of depth data in the warping process and tosimplify the rendering process chorma components are up-sampled to theluma sampling rate. For 4:2:0 data the vertical sampling rate isincreased by a factor of two and the horizontal sampling rate by afactor of eight. This approach allows to process the chroma channels inthe same way as the luma channel. Interpolation filter coefficients arealso taken from HM software version 3.0[5] and are shown in table 2.

TABLE 2 Chroma up-sampling filter from HM software [5] Position Cf. 0Cf. 1 Cf. 2 Cf. 3 Div 1/8 −3 60 8 −1 64 2/8 −4 54 16 −2 64 3/8 −5 46 27−4 64 4/8 −4 36 36 −4 64 5/8 −4 27 46 −5 64 6/8 −2 16 54 −4 64 7/8 −1 860 −3 64

1.2.2 Warping, Interpolation and Hole Filling

In this section only the warping 40 of a left input view to the right ispresented. Warping from right to left can be achieved by reversing alldirections. To increase the processing speed hole filling 48 andinterpolation 42 is integrated in the warping process 40. However, holepositions are marked with 0 in the binary filled map s′_(F) as notfilled by warping. The filled map s′_(F) is used for blending later.

A flow chart of the warping, interpolation and hole filling process isgiven in FIG. 6. Rendering is conducted row-wise, hence the depictedprocess is applied to each row of the input view independently. Theshown steps are carried out for each sample s_(D)(x_(s)) of an inputdepth row from right to left. Hence, processing is conducted iteratingfrom sample position x_(s)=w to sample position x_(s)=1. w denotes inputimage width in samples.

Basic idea of the warping, interpolation and hole filling process isthat rendering of a row is carried out interval wise. In each iterationan interval of the row to be synthesized reaching from x′_(s) to x′_(e)is rendered. x′_(s) and x′_(e) are obtained by shifting two subsequentsamples at positions x_(s) and x_(e)=x_(s)+1 from the input view. Hence,the interval in synthesized view corresponds to the interval starting atx_(s) and ending at x_(e) in the input view. The interval in thesynthesized view is called shifted interval in the following.

Shifting is carried out using

x′=f _(S)(x)=x−s _(Disp)(x)  (13)

with s_(Disp) denoting the actual disparity. From 8-bit input depth datas_(D) in a format as for example used by MPEG [6] the disparity s_(Disp)can be retrieved by

$\begin{matrix}{{s_{Disp}(x)} = {{f \cdot x_{B} \cdot \left\lbrack {{\frac{s_{D}(x)}{255} \cdot \left( {\frac{1}{z_{near}} - \frac{1}{z_{far}}} \right)} + \frac{1}{z_{far}}} \right\rbrack} + x_{doff}}} & (14)\end{matrix}$

with f denoting the focal length of the cameras, x_(B) the baseline ofthe camera pair, and z_(near) and z_(far) the minimal and maximal depthof the depicted scene. x_(doff) is the difference of the offsets betweenthe stereo cameras optical axes and cameras image origins. In thepractical implementation of the renderer eq. (14) is evaluated for allpossible 2⁸ input values of s_(D). Results are stored with quartersample accuracy in a disparity lookup table that is used for the mappingfrom s_(D) to s_(Disp) in the warping process.

In the first step shown in FIG. 6 the shifted position x′_(s) iscomputed using eq. (13). After that it is tested (a) if the currentsample is the last sample position of the input view x_(s)=w. If this istrue the right margin of the view to synthesize is filled as describedin section 1.2.2.2. Subsequently the current shifted position x′_(s) isstored as last shifted position x′_(e) and the current position x_(s) isdecreased by one and processing continues with the next interval.

If x_(s) is not the last position in the input view x′_(s) and x′_(e)provide a shifted interval. It is further investigated if this shiftedinterval is not, partly or entirely occluded. Therefore conditionsmarked with (b), (e) and (d) are evaluated. The result of the evaluationdetermines how processing is continued. All four possible scenarios aredepicted as x′−s_(Disp) charts in FIG. 7. The four possible scenariosare:

-   b_(Occl)=false and x′_(s)≧x′_(e) (x_(s)=4) The Boolean b_(Occl)    signalizes that the last shifted interval is not occluded. However,    the sample from position x_(s) has been shifted to or right to    x′_(e). Hence the samples of the shifted interval are occluded.    x′_(e) is the leftmost shifted position that is occluding other    positions and stored as new minimal occluded position x′_(MinOccl).    Moreover b_(Occl) is set to true and it is checked, if the sample of    the output view near position x′_(e) belongs to the foreground as    described in section 1.2.2.3.-   b_(Occl)=true and x′_(s)>x′_(MinOccl) (x_(s)=3) No rendering or hole    filling is carried out since the whole shifted interval is occluded.    -   b_(Occl)=true and x′_(s)<x′_(MinOccl) (x_(s)=2) The start of the        shifted interval is no longer occluded. b_(Occl) is set to        false. Interpolation or hole-filling is carried out for the        non-occluded part of the shifted interval.-   b_(Occl)=false and x′_(s)>x′_(e)(x_(s)=1) The whole shifted interval    is not occluded. Hence, interpolation or hole filling is carried    out.    Whether rendering or hole filling is performed for the non-occluded    part of a shifted interval depends on the size of the interval (e).    By definition rendering is conducted for intervals with a size    x′_(e)−x′_(s)<=2. The threshold of 2 has been found empirically.    Interpolation of an interval is described in section 1.2.2.1. An    explanation of the hole filling process is given in section 1.2.2.4.

1.2.2.1 Interpolation of a Shifted Interval

In this step all not occluded samples of the current row of synthesizedview s′_(T) in between the start position x′_(s) and the end positionx′_(e) of the shifted interval are rendered. The shifted intervalcorresponds to a interval with start point x_(s) and endpoint x_(e) inthe input view s_(T) and an interval with start point 4·x_(s) andendpoint 4·x_(e) in the up-sampled texture view ŝ_(T). Since s_(Disp) iscalculated with quarter sample accuracy using equation eq. (13) x′_(s)and x′_(e) are given in quarter sample accuracy as well and are mappedto the full sample grid of the synthesized view s′_(T). This mapping isconducted by using

x′ _(s,FP)=ceil(x′ _(s))  (15)

with x′_(s,FP) defining the first sample position in full pa accuracy tobe interpolated and

x′ _(s,FP)=min[ceil(x′ _(e))−1,round(x′ _(MinOccl))−1]  (16)

for the last sample position in full sample accuracy to be interpolated.The term ceil(x′_(e))−1 in eq. (16) fits x′_(s,FP) to the start ofpreviously rendered interval right to the current interval. Taking theminimum of this term and round(x′_(MinOccl))−1 ensures that no occludedsamples are re-rendered again.

After the mapping all sample values for all full sample positionsx′_(FP) from x′_(s,FP) to x′_(e,FP) can be assigned by sample valuesgiven in the up sampled view ŝ_(T). Positions in the up-sampled view canbe retrieved by mapping the positions from the synthesized view s′_(T)to the up-sampled view ŝ_(T) using

$\begin{matrix}{{\hat{x} = {4 \cdot \left( {\frac{x_{FP}^{\prime} - x_{s}^{\prime}}{x_{e}^{\prime} - x_{s}^{\prime}} + x_{s}} \right)}}{{s_{T,l}^{\prime}\left( x_{FP}^{\prime} \right)} = {{\hat{s}}_{T,l}\left( \hat{x} \right)}}} & (17)\end{matrix}$

In the implementation of the renderer this process can be speed up usinga look-up table for the fraction in eq. (17). This is possible since thedistance between x′_(s) and x′_(e) is limited to two. The look-up tablefor quarter sample accuracy is depicted in table 3. Results are roundedto quarter sample accuracy as given in ŝ_(T,l).

x′_(FP) − x′_(s) 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 x′_(e) − 0 0 x x x xx x x x x′_(s) 0.25 0 1 x x x x x x x 0.5 0 0.5 1 x x x x x x 0.75 00.25 0.5 1 x x x x x 1 0 0.25 0.5 0.75 1 x x x x 1.25 0 0.25 0.5 0.50.75 1 x x x 1.5 0 0.25 0.25 0.5 0.75 0.75 1 x x 1.75 0 0.25 0.25 0.50.5 0.75 0.75 1 x 2 0 0.25 0.25 0.5 0.5 0.75 0.75 1 1

Tab. 3 Look-Up Table Realizing the Fraction in Eq.17 with Quarter SamplePrecision

In the case of view interpolation the synthesized depth and the filledmap is needed when blending. Therefore all samples for all samplesx′_(FP) from x′_(x,FP) to x′_(e,FP) are also set in the synthesizeddepth view s′_(D,l) and the filled map s′_(F,l):

s′ _(D,l)(x′ _(FP))=s _(D,l)(x _(s))

s′ _(F,l)(x′ _(FP))=1  (18)

It can be seen that from eq. (18) that only full sample accuracy is usedfor the synthesized depth map.

1.2.2.2 Margin Filling

When extrapolating from a left view to the right information on theright margin of the synthesized view is missing. The rendererextrapolates sample values at these positions by continuing therightmost sample value of the left view by setting

s′ _(T,l)(x′ _(FP))=s _(T,l)(x _(e))=ŝ _(T,l)(4·x _(e))

s′ _(D,l)(x′ _(FP))=s _(D,l)(x _(e))  (19)

for all samples x′_(FP) from x′_(s,FP) to w. Moreover the positionx′_(s,FP) is marked as filled by warping in the filled maps′_(F)(x′_(e,FP))=1 and samples x′_(FP) from x′_(s,FP)+1 to w are markedas not filled by warping s′_(F)(x′_(FP))=0.

1.2.2.3 Extrapolation of Samples Near to Foreground Object

Occlusions appear in the warping process when samples are shifted behinda foreground object. When rendering from left to right this happens ifthe start of the shifted interval is greater or equal to its endx′_(s)≧x′_(e). In this case it may be evaluated whether x_(e,FP) belongsto the foreground object or not. Therefore the condition

x′ _(e,FP)=round(x′ _(e))  (20)

is tested. The correctly rounded leftmost position of the foregroundobject is round(x′_(e)). Hence x′_(e,FP) belongs to the foreground ifeq. (20) is true and

s′ _(T,l)(x′ _(e,FP))=s _(T,l)(x _(e))=ŝ _(T,l)(4·x _(e))

s′ _(D,l)(x′ _(e,FP))=s _(D,l)(x _(e))

s′ _(F,l)(x′ _(e,FP))=1  (21)

are set.

1.2.2.4 Hole Filling

If the width of the shifted interval x′_(e)−x′_(s) is greater than 2 ahole next to the right side of a foreground object is assumed. Similarto evaluation on left foreground object edges as described in section1.2.2.3, it is examined if x′_(s,FP) belongs to the right foregroundobject edge. If x′_(s,FP)=round(x′_(s)) this is true and outputvariables are set according to

s′ _(T,l)(x′ _(s,FP))=s _(T,l)(x _(s))=ŝ _(T,l)(4·x _(s))

s′ _(D,l)(x′ _(s,FP))=s _(D,l)(x _(s))

s′ _(F,l)(x′ _(e,FP))=1  (22)

After that hole filling is carried out by extrapolating the backgroundsample for all x′_(FP) starting from x_(s,FP) or x′_(s,FP)+1 ifx′_(s,FP) belongs to the foreground object to x′_(e,FP). Thereforeoutput variables are set as follows:

s′ _(D,l)(x′ _(FP))=s _(D,l)(x _(e))=ŝ _(T,l)(4·x _(e))

s′ _(T,l)(x′ _(FP))=s _(D,l)(x _(e))

s′ _(F,l)(x′ _(FP))=0  (23)

1.2.3 Blending

If view interpolation is carried out as depicted in FIG. 5, a textureextrapolated from left s′_(T,l) and a texture extrapolated from rights′_(T,r) are blended to create the output synthesized view s′_(T).Additional inputs to blending function are the two synthesized depthmaps s′_(D,l) and s′_(T,r) the two filled maps s′_(F,l) and s′_(F,r).

Since blending is a point operation, instant blending can be carriedout. This means when the sample at position x=x_(e) with the values′_(T,r)(x_(e)) is rendered in the view extrapolation process of theright view, s′_(T)(x_(e)) can directly derived if s′_(T,l)(x_(e)) isalready known and vice versa.

The renderer provides two modes for blending. In the first mode appliesblending using average. This mode uses information from both synthesizedviews equally. In the second mode information from one view is usedmainly. The other view is only used for areas that have not been filledby interpolated samples in the first view.

1.2.3.1 Blending Using Average

Blending is carried out similar to [7], [8] using a distance dependentweighting factor and a decision for the front most sample if aparticular depth-difference threshold is exceeded.

Table 4 gives an overview how the value in the synthesized textures′_(T) is derived from the synthesized textures s′_(T,l) and s′_(T,r).The last column in the table 4 indicates whether s′_(T)(x′) is assignedby s′_(T,l)(x′) or s′_(T,r)(x′) or if distance dependent weighting isperformed using

$\begin{matrix}{{s_{T}^{\prime}\left( x^{\prime} \right)} = {{s_{T,l}^{\prime}\left( x^{\prime} \right)} + {\left\lbrack {{s_{T,r}^{\prime}\left( x^{\prime} \right)} - {s_{T,l}^{\prime}\left( x^{\prime} \right)}} \right\rbrack \cdot \frac{x_{SV} - x_{RV}}{x_{LV} - x_{RV}}}}} & (24)\end{matrix}$

with x_(SV) denoting the horizontal position of the synthesized view andx_(LV) and x_(RV) denoting the position of the left and the right baseview. The distance dependent weighting enables a soft transition of thesynthesized views from the left base view to the right base view.

As shown in table 4 the method for blending depends on the filled mapss_(F,l)(x′) and s′_(F,r)(x′) as well as on the inverse depth differenceb derived from the depth values s′_(Z,l)(x′) and s′_(Z,r)(x′). Theinverse depth values can be calculated from the synthesized input depthvalues using

$\begin{matrix}{\frac{1}{s_{Z}^{\prime}\left( x^{\prime} \right)} = {{\frac{s_{D}^{\prime}\left( x^{\prime} \right)}{255} \cdot \left( {\frac{1}{z_{near}} - \frac{1}{z_{far}}} \right)} + {\frac{1}{z_{far}}.}}} & (25)\end{matrix}$

If the sample value rendered from left s′_(T,l)(x′) and the viewrendered from right s′_(T,r)(x′) are not derived by hole filling asindicated by s′_(F,l)(x′)=1 and s′_(F,r)(x′)=1 the difference of inversedepth

$\begin{matrix}{{b\left( x^{\prime} \right)} = {\frac{1}{s_{Z,l}^{\prime}\left( x^{\prime} \right)} - \frac{1}{s_{Z,r}^{\prime}\left( x^{\prime} \right)}}} & (26)\end{matrix}$

is evaluated.

In the case that absolute value of difference b(x′) is below a thresholdb_(th) view distance dependent blending is carried out as presented ineq. (24). Otherwise it is assumed that the value of the view in thebackground is unreliable and the foreground sample value is take for therendered texture s′_(T)(x′). The threshold b_(th) has been setempirically to

$\begin{matrix}{b_{th} = {0.3 \cdot {\max \left\lbrack {\left( {\frac{1}{z_{{near},l}} - \frac{1}{z_{{far},l}}} \right),\left( {\frac{1}{z_{{near},r}} - \frac{1}{z_{{far},r}}} \right)} \right\rbrack}}} & (27)\end{matrix}$

If only s′_(T,l)(x′) or s′_(T,r)(x′) has been assigned by hole filling,the value of the other view is used in the rendered texture s′_(T)(x′)as shown in rows five and six of table 4. If s′_(T,l)(x′) as well ass′_(T,r)(x′) have been derived by hole filling there is a disocclusionin both views and the extrapolated value of the view in the backgroundis taken for s′_(T)(x′).

TABLE 4 Output sample of s′_(T) depending on filled maps and inversedepth difference s′_(F,l) s′_(F,r) |b| < b_(th) b < 0 s′_(T) 1 1 1 DCBlending 1 1 0 0 s′_(T,l) 1 1 0 1 s′_(T,r) 1 0 DC DC s′_(T,l) 0 1 DC DCs′_(T,r) 0 0 DC 0 s′_(T,r) 0 0 DC 1 s′_(T,l)

1.2.3.2 Blending Using Mainly on View

Table 5 gives an overview how the value in the synthesized textures′_(T)(x′) is derived from the synthesized textures s′_(T,l)(x′) ands′_(T,r)(x′) when mainly blending from the left view.

TABLE 5 Output sample of s′_(T) s′_(F,l) s′_(F,r) s′_(T) 1 1 s′_(T,l) 10 s′_(T,l) 0 1 s′_(T,r) 0 0 s′_(T,l)

Sample values from the view rendered from right s′_(T,r) are only takenwhen a disocclusion occurs in the left synthesized view.

1.2.4 Down-Sampling of Chroma Channels

The last step of processing the conversion from 4:4:4-yuv format usedfor rendering back to 4:2:0 yuv-format. The coefficients of the filterused before down-sampling the color planes by a factor of two inhorizontal and vertical direction are presented in table 6.

TABLE 6 Chroma down sampling filter Cf. 0 Cf. 1 Cf. 2 Div 1 2 1 4

Note that this step is optionally. For the error calculation using therenderer model as described in section 1.3, this step is neglected.

1.3 RENDERER MODEL

This section presents how the renderer proposed in section 1.2 can beextended to the renderer model used for the computation of thesynthesized view distortion change. Therefore the single building blocksdefining the renderer model, as input, output, state, state transitionfunction and output function are discussed. Subsequently it is shown howthe renderer model can be used for multiple input depth maps andmultiple synthesized views.

1.3.1 State

The state of the renderer model is defined by the variables given intable 7. Additionally to new variables s_(O,l) and s_(O,r) are used.s_(O,l) and s_(O,r) are binary maps tracking the occluded input sample.This means s_(O)(x) is 1 when the shifted position of the input sampleat x is occluded by other warped samples. The occlusion maps are neededto recover the variables x′_(MinOccl) and b_(Occl) that are used in therendering process as described in section 1.2.

x′_(MinOccl) and b_(Occl) as well as x′_(MinChg) do not define the stateof the renderer model, but are only auxiliary variables used in therendering process. The same comes true for input textures s_(T,l),s_(T,r) and the reference view s′_(Ref), since these signals areconstant and not altered by state transitions. The state space of therenderer is spanned by all elements of the variables given in table 7.Note that this state space could be reduced to s_(D,l) and s_(D,r), allother state variables are only used to enable fast re-rendering. Due tothe finite number of quantization steps for the state variables therenderer can be modeled as finite state machine.

TABLE 7 Variables defining the state of the renderer model Left ViewRight View Both Views s_(D,l) s_(D,r) Input Depth s_(O,l) s_(O,r)Occlusion Map s′_(D,l) s′_(D,r) Synthesized Depth s′_(T,l) s′_(T,r)s′_(T) Synthesized Texture s′_(F,l) s′_(F,r) Filled Map

1.3.2 Input

The input to render model is defined as show in eq. (28).

(t,v,x _(B,s) ,x _(B,e) ,y _(B,s) ,y _(B,e) ,s _(B))  (28)

t is the input type. The other variables in eq. (28) specify a block Bin one of the depth map s_(D,l) and s_(D,r). v indicates if the block isin the left or the right view. x_(B,s) and x_(B,e) are the horizontalstart and endpoint of the block. The vertical start and endpoints aredenoted by y_(B,s) and y_(B,e). {tilde over (s)}_(B) is a signal of size(x_(B,e)−x_(B,s)+1)·(y_(B,e)−y_(B,s)+1) carrying the new depth data ofthe block.

The renderer model supports two types inputs t to provide two differentfunctionalities. For the first input type the change of the synthesizeddistortion that would be obtained by a change of the specified block Bis given as output. In the process the renderer state remains unchanged.This mode is particularly useful when multiple changes to the modelshould be evaluated before choosing one, as e.g. done in rate distortionoptimization. How the distortion change is calculated is given in sec.1.3.4.

If the second input type is given the renderer model is adapted to thechange of block B by carrying out a state transition as presented in thenext section. No output is produced.

1.3.3 State Transition

A state transition is conducted to adopt the change of the block B givenin the input. Within a transition the samples of a block of the leftinput depth map s_(D,l) or the right depth map s_(D,r) are changed to{tilde over (s)}_(D,l) or {tilde over (s)}_(D,r). As consequence thestate variables are modified resulting in a new synthesized texture{tilde over (s)}′_(T). As before for the renderer, only a change of theleft depth data s_(D,l) is discussed here.

The state transition algorithm consists of four parts: All four parts ofthe algorithm that are successively applied to each row y of the inputblock B starting with y_(B,s) and ending with y_(B,e).

1.3.3.1 Recovery Auxiliary Variables

As presented in section 1.2.2 the rendering process uses the auxiliaryvariables x′_(MinOccl) to track the position of the leftmost sample thatis occluding other samples and b_(Occl) to find out if the last shiftedsample position has been occluded. When rendering a complete row of thesynthesized texture s′_(T) these variables are continuously updatedafter initialization at the right margin of the image x=w. If only a rowof the block B ending at x_(B,e) should be re-rendered x′_(MinOccl) andb_(Occl) are unknown and may be recovered from the render model state.

The flow chart in FIG. 8 depicts the recovery algorithm for x′_(MinOccl)that is used in the case that the end position of the block x_(B,e) isless than the image width w. For x_(B,e)=w the normal initialization ofx′_(MinOccl) and b_(Occl) is applied. It can be seen in FIG. 8 that thealgorithm uses the occluded samples map s_(O). As stated before s_(O)(x)is true for samples at positions x that are shifted to a positionx′=f_(S)(x) that is occluded by other warped samples.

The recovery algorithm utilizes the variable x to perform the search forx′_(MinOccl). Therefore x is set to the end position x_(B,e) of block Bin the first step. After that it is checked if the sample x_(B,e)+1right to x_(B,e) is occluded.

If f_(S)(x_(B,e)+1) is not occluded, indicated by s_(O)(x_(B,e)+1)=0none of the samples right to x_(B,e)+1 are shifted left tof_(S)(x_(B,e)+1), since that would had implied the occlusion off_(S)(x_(B,e)+1). Hence x′_(MinOccl) can be set to the shifted positionf_(S)(x_(B,e)+1).

Note that x′_(MinOccl) might be greater than f_(S)(x_(B,e)+1) in thecase that rendering algorithm starts at sample position w. However, toguarantee a proper transition it is sufficient if rendering fromx=x_(B,e) to x=1 produces the same state as rendering from x=w to x=1.And this is actually given when setting x′_(MinOccl)=f_(S)(x_(B,e)+1).As proven in section 3.1 samples left to x_(B,e)+1 that are shifted toor right to f_(S)(x_(B,e)+1) are anyway occluded. Hence the re-renderingof the row of block B does not depend on x′_(MinOccl) forx′_(MinOccl)≧f_(S)(x_(B,e)+1) if f_(S)(x_(B,e)+1) is not occluded. Anexample for that is depicted in FIG. 9 on the left side. It can be seenfrom the x′−s_(Disp) chart that x′_(MinOccl) is less than the “real”x′_(MinOccl) defined by the leftmost sample of the foreground object.However, due to the relationship from eq. (13) samples can only move onthe diagonal lines shown in the chart. Hence all samples of the changedinterval that are shifted right to x′_(MinOccl) are occluded.

If the evaluation (a) depicted in FIG. 8 shows that the sample atposition f_(S)(x_(B,e)+1) is occluded, some samples right to x_(B,e)+1might occlude positions left to f_(S)(x_(B,e)+1) and a search forminimal occluded position is carried out. Therefore x is incrementedwhile f_(S)(x+1) is occluded as signaled by s_(O)(x+1)=1 and the rightend of the input data has not been reached x+1≦w. Subsequentlyx′_(MinOccl) is derived from the found position x. An example for thisshown in FIG. 9.

In the case that the position x+1 right to the found position x iswithin the input image x+1≦w the minimal occluded position x′_(MinOccl)is set to f_(S)(x+1). Since the sample at x+1 is not occluded, samplesright to x+1 can occluded samples left to f_(S)(x+1). If the foundposition x is equal to the last position in the input image wx′_(MinOccl) is set one quarter sample left to the position left to theshifted position f_(S)(w) as it is done in the normal initializationprocess of the renderer.

b_(Occl) can be set to true if x_(B,e)≧x′_(MinOccl) after the recoveryof x′_(MinOccl). When multiple error calculations related to the sameblock are carried out successively, the recovery process may only becarried out once before the first calculation.

That is, referring to FIG. 9, in processing the intervals (dotted lines)between the pairs of warped texture samples (circles connected by dottedlines), warped from the texture samples of the currently processedportion, occlusions 56 (see FIG. 3) or 80 among the warped texturesamples 50 and the intervals (solid lines) between warped texturesamples (circles connected by solid lines), warped from texture samplesof the second view neighboring the currently processed portion along theprocessing direction, are discovered by continuously updating a firstfarthest—in processing direction 54—extension end (see 60 in FIG. 3) ofpreviously processed intervals among the dashed ones, searching a secondfarthest—in processing direction (54)—extension end (see Fig.x′_(MinOccl)) of the intervals (solid lines) between pairs of warpedtexture samples, warped (40) from a pair of the texture samples (s_(T))of the yet to be processed portions neighboring the current portion in adirection opposite to the processing direction, and detecting occludedpositions of a currently processed interval in case of same lyingupstream relative to the first or second farthest extension inprocessing direction 54.

1.3.3.2 Rendering of a New Data

To minimize computational complexity when re-rendering data from {tildeover (s)}_(D,l) of a row within the block B it is useful to know thestart x′_(CT,s) and the end point of the changed interval x′_(CT,e) inthe synthesized texture. This changed interval not only depends on thenew data {tilde over (s)}_(D,l) but also on the old data s_(D,l) withinthe block B.

The rendering of the new data {tilde over (s)}_(D,l) from x_(B,s) tox_(B,e) affects the synthesized view s′_(T) from {tilde over (x)}′_(C,s)to {tilde over (x)}′_(C,e). As described in section 1.2.2 some samplescan be shifted into occluded areas and the sample order in the input andin the synthesized domain can differ. Therefore it is not sufficient toonly shift the start x_(B,s) and the end x_(B,e) of the input interval.All samples x reaching from x_(B,s) to x_(B,e)+1 are evaluated to find{tilde over (x)}′_(C,s) and {tilde over (x)}′_(C,e) using

{tilde over (x)} _(C,s)=min [f _(S)(x,{tilde over (s)} _(D,l))]  (29)

The last evaluated position in the equations above is x_(B,e)+1 and notx_(B,e), since the rendering is conducted interval wise and the lastinterval is defined as reaching from x_(s)=x_(B,e) to x_(e)=x_(B,e)+1.Similarly rendering using the old data of s_(D,l) from the same inputinterval, results in the output interval from x′_(C,s) to x′_(C,e).

Start and endpoints of the old and new shifted interval can be combinedto derive the start x′_(CT,s) and endpoint x′_(CT,e) of changed intervalin the synthesized domain by

x′ _(CT,s)=min(x′ _(C,s) ,{tilde over (x)}′ _(C,s))

x′ _(CT,e)=min(x′ _(C,e) ,{tilde over (x)}′ _(C,e))  (30)

However, x′_(CT,e) can be further limited, since samples of B that areshifted right to f_(S)(x_(B,e)+1, s_(D,l)) are occluded as proven insection 3.1. These sample do not need to be re rendered and x′_(CT,e)can be set to f_(S)(x_(B,e)+1,s_(D,l)).

An example on how the changed interval is defined depending on thechange of the depth map from x_(B,s) to x_(B,e) is presented in FIG. 10.The changed interval only related to the new depth values is depictedwith broken lines. Note that it is not necessary to re-render samples inbetween {tilde over (x)}′_(C,e) and x′_(C,e). Although this samples arenot updated by rendering the new data, they have been occluded beforethe depth change. However, at the left side of the changed interval,samples from x′_(C,s) to {tilde over (x)}′_(C,s) become visible becausethe foreground edge is shifted to the left by the depth change. Theseuncovered samples are not updated when rendering the new data fromx_(B,s) only. Hence some data of the unchanged depth map left to x_(B,s)may be re-rendered as well.

FIG. 11 depicts the rendering algorithm for changed samples of the blockB. For initialization x′_(e) is set to f_(S)(x_(B,e)+1, s_(D,l)), sincethis is right end of the last changed interval as explained beforemoreover x_(s) is set to x_(B,e).

A comparison of the flow chart for rendering as presented in FIG. 11shows three new processing steps. The computation of the minimal changedposition x′_(MinChg)(x) is the first difference. x′_(MinChg)(x) iscomputed using eq. (31).

x′ _(MinChg)(x _(s))=min[f _(S)(x _(s) ,s _(D,l)),f _(S)(x _(s) ,{tildeover (s)} _(D,l)),x′ _(MinChg)(x _(s)+1)]  (31)

Eq. (31) is the iterative solution of eq. (29) and eq. (30). Hence afterall samples of the row within block B are processed and x_(s) is equalto x_(B,s), the minimal changed position x′_(MinChg)(x_(B,s)) is equalto x′_(CT,s). x′_(MinChg)(x_(B,s)) is used in the next part of the statetransition to terminate the rendering process.

The other two new steps in FIG. 11 are the assignments to the occlusionmap s_(O). If the sample at position f_(S)(x_(s)) is occluded in thesynthesized view, s_(O)(x_(s)) is set to true, otherwise to false. Thelast decision (f) in FIG. 11 shows, that this part of the renderingprocess is terminated after the leftmost sample of the row of the blockB has been processed.

1.3.3.3 Rendering of Data Next to New Data

With the rendering of data of a row of {tilde over (s)}_(D,l) withinx_(B,s) and x_(B,e) positions from {tilde over (x)}′_(C,s) to {tildeover (x)}′_(C,e) are altered in the synthesized texture s′_(T). Howeverfor x′_(CT,s)<{tilde over (x)}′_(C,s) some samples left to {tilde over(x)}′_(C,s) are also altered and samples left to x_(B,s) may bere-rendered as well. How this is done is shown in the flowchart in FIG.12.

In the first iteration the end x′_(e) of the shifted interval isf_(S)(x_(B,s),{tilde over (s)}_(D,l)) as assigned in the last steps ofpart two. In contrast to the rendering of the new data, the update ofx′_(MinChg) can be omitted. Furthermore the case x_(s)=w is not possibleany more. Hence steps related to that can be omitted as well. At the endof the rendering of a shifted interval it is checked whether its startposition x_(s) is less than the minimal changed position x′_(MinChg). Inthis case the complete changed interval in the synthesized has beenre-rendered and the rendering process of this line can be terminated.

Note that re-rendering data right to x_(B,e) is not necessary for tworeasons already mentioned above. The first reason is that samples leftto x_(B,e)+1 are occluded when shifted right to f_(S)(x_(B,e)+1) hencethe changed data cannot interfere data right to x_(B,e)+1. The usage ofthe x′_(MinOccl) variable is the second reason. Samples right to x_(B,e)can occlude samples left to f_(S)(x_(B,e)), however with help ofx′_(MinOccl) these occluding samples are left unchanged when renderingthe changed data.

1.3.3.4 Adoption of New Depth Values

In the last part of the state transition the next transition is preparedby assigning the changed depth values from {tilde over (s)}_(D,l) tos_(D,l).

1.3.4 Output

If the input type t is set to produce an output the state of therenderer model remains unchanged. The input to the model is only used tocompute the change of the global synthesized view distortion, caused bythe change of the depth data within block B.

A simple way to achieve such a behavior would to carry out a statetransition to produce the changed synthesized view for the computationof the error change. However, this would involve storing the currentrenderer state before state transition and to reset it afterwards. In apractical implementation this storing and restoring is associated withmultiple memory accesses and high computational complexity. Moreover itis not know beforehand which elements of the state variables are changedand need to be stored.

To avoid these issues the renderer model is designed in a way that theerror calculation can directly be conducted without altering elements ofthe renderer state variables. This property is already reflected in thestate transition process as described in the last section. An analysisof this process shows that all decisions conducted there when renderingan interval do not rely on elements of state variables of the new staterelated to other intervals. Only data of the old state and the input areutilized together with the intermediate variables created for thecurrent interval.

Therefore the state transition algorithm can be easily converted to anerror calculation algorithm by two modifications. The first modificationis that no assignments to the state variables are executed. The othermodification is that error calculation is carried out in all steps thatwould alter the synthesized output texture in a state transition. Hence,the change of the global synthesized view distortion is calculatedinstantly after blending a sample. The change of distortion can then becalculated by carrying out the integration in eq. (32) iteratively fromx′_(CT,e) to x′_(CT,s) while calculating {tilde over (s)}′_(T)(x).

$\begin{matrix}{{\Delta \; D} = {\sum\limits_{x^{\prime} = x_{{CT},s}^{\prime}}^{x_{{CT},s}^{\prime}}\left( {\left\lbrack {{{\overset{\sim}{s}}_{T}^{\prime}\left( x^{\prime} \right)} - {s_{Ref}^{\prime}\left( x^{\prime} \right)}} \right\rbrack^{2} - \left\lbrack {{s_{T}^{\prime}\left( x^{\prime} \right)} - {s_{Ref}^{\prime}\left( x^{\prime} \right)}} \right\rbrack^{2}} \right)}} & (32)\end{matrix}$

Note that ΔD can be negative as well as positive. To reducecomputational complexity in a practical implementation of the algorithm,it is also possible to compute [s′_(T)(x′)−s′_(Ref)(x′)]² from eq. (32)already in the state transition and to and store the result asadditional state variable holding the current distortion per sample.

Distortion computation for the up-sampled chroma channels is treatedlikewise. However, in the total distortion sum u- and v-distortion areweighted by one quarter while the weight of the luma channel is one.

1.3.5 Multiple Views

The model presented so far is designed for a left and a right input viewand one synthesized output view. However, scenarios with multiple inputand multiple output views are possible as well. Distortion computationin multiple synthesized views can be carried out by using one renderermodel per output view. The state variables s_(D,l) and s_(D,r) can beshared by all models with synthesized views in between the left and theright view. For more than two input views s_(D,l) of one model can beequal to s_(D,r) in another model or vice versa.

An example with three input views and four synthesized views is depictedin FIG. 13. Models M1 and M2 calculate the distortion for twosynthesized views in between V1 and V2, whereas models M3 and M4 areused for the distortion computation of two views in between V2 and 173.Model M1 and M2 as well as model M3 and M4 share the same s_(D,l) ands_(D,r). Moreover depth of V2 is s_(D,r) in model M1 and M2 and s_(D,l)in model 113 and M4. The total distortion change can be obtained bysumming up ΔD₁ to ΔD₄.

1.4 CONCLUSION

An embodiment for the synthesized view distortion computation has beenpresented that can be utilized in the processing of depth data likedepth estimation, depth filtering and depth coding.

Unlike other methods, which only provide an estimate of the synthesizedview distortion, the embodiment described above provides the correctchange of the total synthesized view distortion related to a change ofdepth data. The calculation of the total synthesized view distortioninvolves a complete synthesized view, hence a complete depth map isneeded, even if only the distortion of a depth block should beevaluated. Therefore the already processed depth is assumed in alreadyprocessed parts of the depth map and original depth data in thenon-processed regions.

For view synthesize a simple rendering algorithm is used providing thebasic features of more complex approaches, like view interpolation andview extrapolation, sub pixel accurate rendering, line wise hole fillingand distance dependent blending with front most decision or usage ofmainly one view. In contrast to other approaches these features arefully regarded in the distortion computation.

To reduce computational complexity the embodiment outlined above onlyre-renders or calculates the distortion in parts that are affected bythe depth change. This is carried out by the renderer model. Keyfeatures to increase the processing speed are:

-   Storage of intermediate data: Intermediate data of the rendering    process is stored as state of the renderer model and re-used.-   State transition or error calculation: A state transition is carried    out to adapt the renderer model to finally processed depth data.    This triggers the re-rendering of the corresponding changed part of    the synthesized view and modifies the stored intermediate variables.    In the error calculation mode the synthesized view distortion is    provided without altering the renderer model state. Hence, multiple    depth changes can be evaluated rapidly without resetting the state    transitions.-   Instant occlusion handling: Occlusion handling is integrated to the    warping process. Instead of using complex z-buffer methods,    background samples are identified by their shifted position.-   Instant hole filling: Holes are identified and filled within warping    process. For interpolation hole positions are additionally marked    and possibly filled from the second view when blending. In contrast    to other approaches the instant hole filling enables the    extrapolation from occluded background neighbor samples.-   Sub-sample accuracy using pre-interpolation: The texture data is    interpolated, when initializing the renderer model. In the warping    process positions of the synthesized view are only mapped to    positions of the up-sampled texture data.-   Instant blending: As soon as a view's sample is rendered in the    warping process it is blended with the sample from the other view.-   Instant error calculation: If the renderer model shall provide the    synthesized view distortion, the error for a sample is directly    computed, when the new sample is rendered.-   Interval-wise rendering All processing steps of renderer are    integrated to an algorithms that processes the changed depth map by    carrying out one iteration per sample. Likewise each changed sample    of the output view is updated one time in the rendering process.-   Minimal re-rendering The changed interval in the synthesized view is    determined while warping. When all changed samples in the    synthesized view have been updated the re-rendering process is    stopped.-   Parallelization: Rendering can be carried out for each row    independently. Hence parallelization is possible.

2 VIEW SYNTHESIS DISTORTION CHANGE BASED ENCODING

This chapter organizes as follow: In section 2.1 it is described how therender model may be integrated in the rate-distortion optimization ofthe HM encoder software. Moreover it is explained in section 2.2 howreference views for the encoding processed can be derived.

2.1 Integration of the Render Model in the HM Encoder

In this section it is described how the renderer model is integrated inthe rate-distortion optimization of the HM encoder software 3.0. Sincethe renderer model has to be in the correct state to provide a correctdistortion, it is not sufficient to only replace distortion calculationmethods. State transitions of the renderer model may be triggered by theencoder, when decisions on how to encode a block have been made or whenalready done decisions are withdrawn. The conventional rate-distortionoptimization in the HM Encoder is described in section 2.1.1. After thatmodification conducted to integrate the renderer model to the encoderare presented in section 2.1.2.

Since the renderer model provides a new distortion calculation metric,the Lagrange multiplier may be adapted as well to optimize the resultsattained using the renderer model. Section 2.1.3 provides informationhow this has been conducted.

2.1.1 Rate-Distortion Optimization in the HM Encoder

FIG. 14 gives a rough overview of the rate-distortion optimization ofthe HM encoder software version 3.0[5]. The figure shows a structogramcontaining the single steps and decisions needed to compress a singlecoding unit (CU). Steps related to the optimization of the synthesizedview are placed against a gray background and not part of the originalalgorithm. These steps are discussed in the next section 2.1.2.

Decisions in the encoding process are made based on the rate-distortioncost J defined as

J=D+λ·R  (33)

with D and R denoting the distortion and rate of the currently evaluatedblock and mode. λ is the Lagrange multiplier depending on thequantization parameter and the slice type. As depicted in FIG. 14 theencoding process of a CU is hierarchical. Results of taken decisionslike rate and distortion are passed from the lower levels performing theencoding of the residual quadtree (inter QT coding, intra QT coding) tothe top level (compress CU). The single building blocks are:

-   compress CU: At the top level a check of the merge mode, four    different inter partitions (2N×2N, N×N, 2N×N, N×2N) and two    different intra partitions (2N×2N, N×N) is executed. Within each    check the encoder compares one or multiple modes to the currently    best mode carrying out a rate-distortion based decision. The winner    of this test is stored as new best mode. In the structogram this    testing step is denoted as “check and set best”. After testing all    inter and intra partitions, it is tested if a split of the CU in    four sub-CUs yields a better rate-distortion performance. Therefore    each sub-CU is recursively compressed before comparing the total    rate-distortion cost of all four sub-CUs to the currently best    costs.-   check merge: When checking the merge mode all suitable merge    candidates are tested with and without residual and the best result    is preserved.-   check inter: Motion vectors are estimated for all parts of the CU.    Details of the motion estimation are not explicitly shown in the    structogram. However, the estimation is carried out based on    rate-distortion cost testing different reference pictures as well as    P and B prediction. Rate-distortion costs used in inter residual    coding are not exact, but only estimations. Hence, exact costs are    obtained by encoding the motion vectors and the residual    subsequently to the motion estimation.-   inter coding: Inter coding can be tested with and without skipping    the residual. If the CU is compressed without residual, the    distortion is computed in the next step. For non-skip modes it is    possible to test different quantization parameters offsets (AQPs)    when compressing the residual quadtree. Since inter quadtree coding    returns an approximated distortion from unclipped signal vales only,    the distortion is exactly re computed in the last step.-   inter QT coding: This building block estimates recursively a    rate-distortion optimized quadtree structure to compress the    residual. A block of the residual can either be coded fully or split    up in four parts. Moreover it is possible to skip the residual for    each part independently. Therefore the compression of the full block    is checked with and without residual first. The best result and the    rate-distortion costs are stored. Subsequently, a further split is    checked recursively, if the highest partitioning depth, has not been    reached yet. If splitting does not result in better costs the    results of coding the full block is restored afterwards.-   check intra: For intra CUs all PUs are optimized successively. To    minimize computational complexity the optimization is carried out in    a three-step approach. First all modes are tested using the rate for    mode signaling and distortion of the prediction only. A small number    of best modes are stored for further investigation. In the second    step these stored modes are tested using a quadtree without    splitting. All modes, but the two best modes are rejected. In the    last step the best mode is chosen out of this two, based on a test    considering a quadtree of full depth.-   intra QT coding: Encoding of the intra quadtree is similar to the    encoding of the inter quadtree. A difference is that it is not    tested, whether the residual should be skipped.

2.1.2 Modifications of the Rate-Distortion Optimization

To enable rate-distortion optimization using the synthesized viewdistortion the renderer model is integrated in the encoding process.Therefore conventional distortion computation carried out while encodingis replaced with computation of the global distortion change ofsynthesized view in all distortion computation steps depicted in FIG.2.1.2. However, to reduce computational complexity the render model isnot used in the motion estimation step, here.

To provide valid distortion changes the renderer model has to be in thecorrect state. Hence, the input depth map state variable of the renderermodel may incorporate the coded depth data of all previously codedblocks and original depth data of all other blocks. To achieve this, therenderer model is continuously updated while encoding. This is done bythe steps highlighted gray in FIG. 2.1.2. Steps denoted “set RM” meanthat change of the currently evaluated depth block is give as input tothe renderer model to perform a state transition. Steps named “reset RM”also conduct a state transition of the renderer model. However, here thecurrent depth block is reset to original input data. In the following itis discussed when depth data is set or reset in the renderer model.

When encoding the residual signal the depth data of the renderer modelis set for each block of the CU belonging to a leaf of the residualquadtree. Hence, when encoding a node of the tree, depth data belongingto already encoded siblings is up to date in the renderer model.

To encode the same block of depth data in a different mode, or withother parameters it is useful to reset the data of the block. For intercoding this is done subsequently to the compression of the quadtreebefore encoding with another quantization parameter in the “interresidual coding” block. For intra coding this reset is carried out forbefore a new PU is coded in the stages of the mode decision refinementprocess. After the optimal mode for a PU has been found in the intracheck, the coded data the PU is set in the renderer model, beforecompressing the next PU.

Moreover it can be seen in FIG. 2.1.2 that the complete CU is reset atthe begin of checking a merge candidate, the inter modes and the intramodes. This is done to ensure that all data potentially set by tests ofmodes carried out before is reset.

When checking if the CU is split up in the top level block (“compresssCU”) a reset is performed as well. The result of the optimization of asub-CU is set in the renderer model in the sub-CU checking loop, toensure a correct renderer state for the following sub-CUs.

Finally, as last step in the (“compress CU”) block the result of theoptimization is set in the renderer model before continuing with thenext CU.

2.1.3 Lagrange Multiplier Optimization

The usage of synthesized view distortion in rate-distortion decisionsinvolves the adaptation of the Lagrange multiplier λ to obtain optimalencoding result. This adaptation is carried out in two step approach. Inthe first step the Lagrange multiplier is adjusted roughly using aconstant factor. A fine tuning using a factor depending on thequantization parameters conducted in the second step.

For the rough adaptation rate-distortion cost computation, as presentedin eq. (33) has been modified to

JγΔD+l _(s) ·λ·R  (34)

with ΔD denoting the change of global synthesized view distortion asprovided by the renderer model and l_(s) as constant scaling factor.Coding experiments show that l_(s)=0.5 provides good results for highquantization parameters.For the exact optimization a quantization parameter dependent scalingfactor has been determined by coding experiments.

2.2 Synthesized View References

As described in section 1.1.1 the renderer model uses a reference views′_(Ref) for distortion calculation. This reference view can be anoriginal view or a rendered view. Whether an original view or a renderedview should be used depends on the use case.

Intermediate original views are often not available, hence anoptimization can only be carried out by warping the left original viewto the right original view and vice versa. Such an optimization leads toa rate constraint depth re-estimation carried out by the encoder.Although it is possible that depth error in the initial depth maps arereduced, it is also possible that information in the depth mapsretrieved by more complex depth estimation approaches are reduced aswell. This is especially true for areas that are occluded in theoriginal view and might lead to rendering artifacts when synthesizingintermediate views.

Rate-distortion optimization utilizing a rendered reference views yieldsbetter preservation of the original synthesized views. Moreover multipleintermediate views can be used. However, one drawback is that renderingartifacts due to already existing errors in the depth map are preservedas well. In the following the usage of rendered reference views isdiscussed for the cases of view extrapolation and view interpolation.

2.2.1 View Extrapolation

Eq. (2) shows that distortion calculation is carried out by a comparisonof the rendered reference view to s′_(Ref) to the distorted view {tildeover (s)}′_(T). Moreover it can be seen from eq. (1) that theextrapolated view depends on a depth map and a video. This raises thequestion, if coded or uncoded depth and video data should be used torender s′_(Ref) and {tilde over (s)}′_(T). Since the depth data is notcoded yet, original data s_(D) are used for the generation of thereference view, whereas the partly coded depth map s′_(T) is used forrendering {tilde over (s)}′_(T) as described above. Assuming that thevideo data of the view has been coded before the depth data, it ispossible to use coded or uncoded texture data for rendering of thereference texture and the texture {tilde over (s)}′_(T). All fourpossibilities are depicted in FIG. 15.

Combination (a) uses the original texture data for rendering {tilde over(s)}′_(T) and s′_(Ref). The approach is especially suitable if theencoding of the depth should not depend on the texture coding.Nevertheless, distortions caused by the coded texture are neglected. Acomparison of {tilde over (s)}′_(T) rendered with coded texture datacompared to s′_(Ref) rendered with original data is carried out whenusing combination (b). The total distortion includes not only thedistortion of the depth, but also distortions caused by the texturecoding. However, since the renderer model only regards distortionchanges ΔD caused by a depth change this bias does not infer therate-distortion optimization. Theoretically it is possible for thiscombination that the encoding of depth data reduces the distortion dueto coded texture. An example for this are distorted video samples thatbecome occluded, when encoding the depth data. Using the coded textureto render the reference s′_(Ref) and the uncoded for the view to test{tilde over (s)}′_(T) as done for combination (e) has no practical use.For the last combination (d) {tilde over (s)}′_(T) and s′_(Ref) are bothrendered from the coded texture. Hence, the influence of the codedtexture can be regarded in the encoding process although the totaldistortion is not biased by the texture distortion. This approach hasthe advantage that signal parts in the depth data related to signalparts or noise in the original texture and removed by encoding areneglected when encoding the depth data.

Evaluations show that combination (b) yields the highest gains.

2.2.2 Interpotation

For view interpolation two textures and two depth maps are used as shownin equation eq. (12). Similar to the extrapolation case, there aremultiple combinations possible in the rate-distortion optimization forrendering the reference view and the view to test. These combinationsare discussed in the following. For simplification it is assumed thatcoding is carried out in the order: left video s_(T,l), left depths_(D,l), right video s_(T,r) and right depth s_(D,r).

When encoding the first (left) depth map s_(D,l) the correspondingtexture s_(T,l) has already been coded and texture s_(T,r) and depths_(D,r) of the right view is still uncoded. Hence, if interpolationshould be carried out this has to be performed using the original videoand depth data of the right view. In the blending step the rendereddistorted left view {tilde over (s)}′_(T,l) is then blended with aundistorted rendered right view s_(T,r). This leads to a reduction ofdistortion change ΔD obtained in the optimization. Note, that the usageof the uncoded data of the right view is in line with the conceptapplied generally in the renderer model. Whilst block wise evaluationthe render model utilizes original data from uncoded blocks, hence usinguncoded data of the right view extents this concept. For rendering thereference view s′_(Ref) and the view to test {tilde over (s)}′_(T) it ispossible to use the coded or the uncoded left texture s′_(T,l). Thus thesame combinations as presented for view extrapolation are applicable.

An alternative to rendering using the original data of the right view isto disregard this view and to carry out extrapolation. This approachneglects the blending process and guarantees an optimized shifted leftview s′_(T,l). In contrast to the shifted left view obtained fromassuming original data for the right view, this shifted left view mightbe a more reliable base for rendering the synthesized view s′_(T), sinceit is not know which kind of distortion will be introduced when encodingthe data of the right view.

When encoding the second depth s_(D,r) the corresponding texture s_(T,r)and texture s_(T,l) and depth s_(D,l) of the left view have already beencoded. For all three signals the coded or the uncoded data can beemployed to render s′_(T) and s′_(Ref). This gives eight possibilitiesto render s′_(T) and eight possibilities to render s′_(Ref) and leads to64 possible combinations that could be utilized in the rate-distortionoptimization process. However, most of these combinations are notsuitable for the rate-distortion optimization. Additional it is, likefor the first view, possible to ignore the left view, when optimizingthe depth data of the right view. The blending step in rendering isneglected and the left view is extrapolated from the right view.

An overview of three feasible methods to generate the reference and theview to test selected from numerous possible combinations is given inFIG. 16.

For all methods the reference views are generated from uncoded textureand depth data. Method (a) performs an independent coding of the leftand the right view. The reference views and the views to test areextrapolated. For the views to test the already coded textures are used.In method (b) extrapolation carried out only when encoding the leftdepth, since coded data for the right view is not available. Whenencoding the right view interpolation of the view to test is conductedusing the already coded texture and depth data from the right view.Method (e) uses interpolation for encoding the left and the right view.Since no coded data of the right view is available when encoding theleft view, original texture and depth data is utilized. To perform theencoding of the depth data independent from the encoding of texturedata, it is also possible to replace the coded texture {tilde over(s)}_(T,l) and {tilde over (s)}_(T,l) data with uncoded data s_(T,l) ands_(T,r) for all three methods.

An evaluation of all six possibilities has been conducted. It was foundthat combination (e) using encoded texture data yields the bestrate-distortion performance.

3 APPENDIX 3.1 Proof

The proof is valid for rendering from a left view to create asynthesized right view. However the other direction can be proven in thesame manner. It is shown that a input sample at position x that isshifted to f_(S)(x) is occluded if f_(S)(x)≧f_(S)(x+1).

$\begin{matrix}\begin{matrix}\; & {{f_{S}(x)} \geq {f_{S}\left( {x + 1} \right)}} \\\Leftrightarrow & {{x - {s_{Disp}(x)}} \geq {x + 1 - {s_{Disp}\left( {x + 1} \right)}}} \\\left. \;\Rightarrow \right. & {{s_{Disp}(x)} \leq {s_{Disp}\left( {x + 1} \right)}} \\\Leftrightarrow & {\frac{f \cdot x_{B}}{s_{Z}(x)} \leq \frac{f \cdot x_{B}}{s_{Z}\left( {x + 1} \right)}} \\\Leftrightarrow & {{s_{Z}(x)} \geq {s_{Z}\left( {x + 1} \right)}}\end{matrix} & (35)\end{matrix}$

It can be concluded that depth at position s_(Z)(x) is greater than orequal to the depth at position s_(Z)(x+1). Hence the sample at positionx is occluded in the synthesized view. Note it also assumed thatbackground samples left of a foreground object in the input view do notappear in a disocclusion at the right side of foreground in thesynthesized view.

Thus, a concept for the fast computation of distortion in one ormultiple views synthesized from multi-view plus depth data has beenpresented in the above embodiment. The algorithm can be utilized in theestimation, filtering or compression of depth data. Unlike other methodsthat estimate the distortion in synthesized views caused by a distortionof depth data the above embodiment computes the exact distortion changeof the synthesized view using a simple rendering algorithm. Henceeffects of occlusion, disocclusion, blending and hole filling areregarded. For complexity reduction the distortion computation is carriedout by only re-rendering of parts of synthesized view that are affectedby a change of the depth data. The rendering process is modeled as afinite state machine accepting depth changes as input, holding thecurrent rendering state, and giving the synthesized view distortionchange as output. It has been discussed how the renderer model can beintegrated to the HM software encoder. Different methods to createsynthesized reference textures for the encoding process are presented.

Although some aspects have been described in the context of anapparatus, it is clear that these aspects also represent a descriptionof the corresponding method, where a block or device corresponds to amethod step or a feature of a method step. Analogously, aspectsdescribed in the context of a method step also represent a descriptionof a corresponding block or item or feature of a correspondingapparatus. Some or all of the method steps may be executed by (or using)a hardware apparatus, like for example, a microprocessor, a programmablecomputer or an electronic circuit. In some embodiments, some one or moreof the most important method steps may be executed by such an apparatus.

Depending on certain implementation requirements, embodiments of theinvention can be implemented in hardware or in software. Theimplementation can be performed using a digital storage medium, forexample a floppy disk, a DVD, a Blu-Ray, a CD, a ROM, a PROM, an EPROM,an EEPROM or a FLASH memory, having electronically readable controlsignals stored thereon, which cooperate (or are capable of cooperating)with a programmable computer system such that the respective method isperformed. Therefore, the digital storage medium may be computerreadable.

Some embodiments according to the invention comprise a data carrierhaving electronically readable control signals, which are capable ofcooperating with a programmable computer system, such that one of themethods described herein is performed.

Generally, embodiments of the present invention can be implemented as acomputer program product with a program code, the program code beingoperative for performing one of the methods when the computer programproduct runs on a computer. The program code may for example be storedon a machine readable carrier.

Other embodiments comprise the computer program for performing one ofthe methods described herein, stored on a machine readable carrier.

In other words, an embodiment of the inventive method is, therefore, acomputer program having a program code for performing one of the methodsdescribed herein, when the computer program runs on a computer.

A further embodiment of the inventive methods is, therefore, a datacarrier (or a digital storage medium, or a computer-readable medium)comprising, recorded thereon, the computer program for performing one ofthe methods described herein. The data carrier, the digital storagemedium or the recorded medium are typically tangible and/ornon-transitionary.

A further embodiment of the inventive method is, therefore, a datastream or a sequence of signals representing the computer program forperforming one of the methods described herein. The data stream or thesequence of signals may for example be configured to be transferred viaa data communication connection, for example via the Internet.

A further embodiment comprises a processing means, for example acomputer, or a programmable logic device, configured to or adapted toperform one of the methods described herein.

A further embodiment comprises a computer having installed thereon thecomputer program for performing one of the methods described herein.

A further embodiment according to the invention comprises an apparatusor a system configured to transfer (for example, electronically oroptically) a computer program for performing one of the methodsdescribed herein to a receiver. The receiver may, for example, be acomputer, a mobile device, a memory device or the like. The apparatus orsystem may, for example, comprise a file server for transferring thecomputer program to the receiver.

In some embodiments, a programmable logic device (for example a fieldprogrammable gate array) may be used to perform some or all of thefunctionalities of the methods described herein. In some embodiments, afield programmable gate array may cooperate with a microprocessor inorder to perform one of the methods described herein. Generally, themethods are advantageously performed by any hardware apparatus.

While this invention has been described in terms of several embodiments,there are alterations, permutations, and equivalents which fall withinthe scope of this invention. It should also be noted that there are manyalternative ways of implementing the methods and compositions of thepresent invention. It is therefore intended that the following appendedclaims be interpreted as including all such alterations, permutationsand equivalents as fall within the true spirit and scope of the presentinvention.

REFERENCES

-   [1] A. Smolic, K. Mueller, P. Merkle, P. Kauff, and T. Wiegand, An    overview of available and emerging 3D video formats and depth    enhanced stereo as efficient generic solution, in Proceedings of the    27th conference on PCS, (Piscataway, N.J., USA), pp. 389-392, 2009.-   [2] B. T. Oh, J. Lee, and D.-S. Park, Depth map coding based on    synthesized view distortion function, Selected Topics in Signal    Processing, IEEE Journal of, vol. 5, pp. 1344-1352, November 2011.-   [3] W.-S. Kim, A. Ortega, P. Lai, D. Tian, and C. Gomila, Depth map    distortion analysis for view rendering and depth coding, pp.    721-724, nov. 2009.-   [4] W.-S. Kim, A. Ortega, P. Lai, D. Tian, and C. Gomila, Depth map    coding with distortion estimation of rendered view, in Society of    Photo-Optical Instrumentation Engineers (SPIE) Conference Series,    vol. 7543 of Society of Photo-Optical Instrumentation Engineers    (SPIE) Conference Series, January 2010.-   [5] HEVC Test Model 3 (HM 3) Encoder Description (MPEG/N20270),    ISO/IEC JTC1/SC29/WG11, 2011.-   [6] Report on experimental framework for 3D video coding    (MPEG/N11631), 2010.-   [7] Reference Softwares for Depth Estimation and View Synthesis    (MPEG/N15377), ISO/IEC JTC1/SC29/WG11, 2008.-   [8] View Synthesis Reference Software (VSRS) 3.5, wg11.sc29.org,    March 2010.

1. An apparatus for determining a measure for a distortion change of afirst view synthesized from a second view, caused by a modification of adepth map of the second view from a first state to a second state, theapparatus being configured to starting from a current synthesis state ofthe first view corresponding to a synthesis from the second viewcomprising the depth map modified to the second state in an alreadyprocessed portion of the depth map and comprising the depth mapunmodified at the first state in a yet to be processed portion of thedepth map, compute a possible successor synthesis state corresponding toa synthesis of the first view from the second view comprising the depthmap modified to the second state in an already processed portion plus acurrently processed portion and comprising the depth map unmodified atthe first state in the yet to be processed portion without the currentlyprocessed portion; determine a distortion change of a distortion of thecurrent synthesis state of the first view relative to an undistortedversion of the first view to a distortion of the possible successorsynthesis state of the first view relative to the undistorted version ofthe first view.
 2. The apparatus according to claim 1, wherein theapparatus is configured to initially determine a synthesis of the firstview from the second view comprising the depth map completely unmodifiedat the first state so as to acquire the undistorted version of the firstview.
 3. The apparatus according to claim 1, wherein the apparatus isconfigured to restrict the computation and the determination to asection of the first view within which changes may occur between thecurrent synthesis state and the possible successor synthesis state. 4.The apparatus according to claim 1, wherein the apparatus is configuredto, in performing the determination, use a per-pixel texture differencemeasure as a measure for the distortion of the synthesis state.
 5. Theapparatus according to claim 1, wherein the apparatus is configured to,in performing the computation and determination, warp texture samples ofthe currently processed portion from the second view into the first viewusing the modified second state of the depth map and determine thedistortion of the possible successor synthesis state of the first viewas defined by an interpolation of the warped texture samples onto samplepositions of the first view, relative to the undistorted version of thefirst view, in a processing direction contrary to a rendering directionpointing from a view point of the second view to a view point of thefirst view.
 6. The apparatus according to claim 5, wherein the apparatusis configured to, in interpolating the warped texture samples onto thesample positions of the first view, perform hole filling and/or blendingwith another view.
 7. The apparatus according to claim 5, wherein theapparatus is configured to, in performing the computation anddetermination, process intervals between pairs of the warped texturesamples, warped from a pair of the texture samples of the currentlyprocessed portion using the modified second state of the depth map,immediately neighboring each other in the second view, at an orderaccording to which the pairs of texture samples are arranged along theprocessing direction.
 8. The apparatus according to claim 5, wherein theapparatus is configured to, in processing the intervals between thepairs of warped texture samples, compute a per-pixel texture differencemeasure to the undistorted version of the first view for samplepositions of the first view covered by a respective interval beforeproceeding to the next interval in the processing order.
 9. Theapparatus according to claim 8, wherein the apparatus is configured to,in processing the intervals between the pairs of warped texture samples,obey occlusions among the warped texture samples, warped from thetexture samples of the currently processed portion, and the warpedtexture samples, warped from texture samples of second view neighboringthe currently processed portion along the processing direction so thatoccluded warped texture samples do not contribute to the distortion ofthe possible successor synthesis state.
 10. The apparatus according toclaim 8, wherein the apparatus is configured to, in processing theintervals between the pairs of warped texture samples, discoverocclusions among the warped texture samples, warped from the texturesamples of the currently processed portion, and the warped texturesamples, warped from texture samples of second view neighboring thecurrently processed portion along the processing direction, continuouslyupdate a first farthest—in processing direction—extension end ofpreviously processed intervals, search a second farthest—in processingdirection—extension end of intervals between pairs of warped texturesamples, warped from a pair of the texture samples of the yet to beprocessed portions neighboring the current portion in a directionopposite to the processing direction, and detect occluded positions of acurrently processed interval in case of same lying upstream relative tothe first or second farthest extension in processing direction.
 11. Theapparatus according to claim 7, wherein the apparatus is configured tocontinue processing the intervals between the pairs of warped texturesamples, warped from a pair of the texture samples of the currentlyprocessed portion using the modified second state of the depth map, inthe processing direction to intervals between pairs of warped texturesamples, warped from a pair of the texture samples of the alreadyprocessed portion using the modified second state of the depth map,until an interval which in the processing direction, protrudes, in theprocessing direction, over an outermost—in the processing direction—endamong the intervals between the pairs of warped texture samples, warpedfrom a pair of the texture samples of the currently processed portionusing the modified second state of the depth map, and intervals betweenpairs of warped texture samples, warped from a pair of the texturesamples of the currently processed portion using the unmodified firststate of the depth map.
 12. The apparatus according to claim 1, whereinthe apparatus is configured to output the distortion change to a depthmodifier, repeat the computation, the determination and the output fortrials of different modifications of the depth map at the currentlyprocessed portion of the depth map of the second view on behalf of thedepth modifier, with, for each repetition, starting the computation fromthe current synthesis state so as to acquire a respective possiblesuccessor synthesis state per different modification, update, upon afinal selection by the depth modifier, the current synthesis state tocorrespond to the possible successor synthesis state of a finallyselected modification of the depth map at the currently processedportion, and repeat the computation, the determination, the output andthe update for a subsequently processed portion with starting thecomputation from the updated synthesis state.
 13. The apparatusaccording to claim 12, wherein the apparatus is configured to performthe updating the current synthesis state to correspond to the possiblesuccessor synthesis state of a finally selected modification of thedepth map at the currently processed portion such that the updatedsynthesis state comprises the warped texture samples warped from thetexture samples of the currently processed portion from the second viewinto the first view using the selected modification of the depth map, atsub-pel resolution.
 14. The apparatus according to claim 12, wherein thedepth modifier is a lossy multi-view encoder, a depth encoder, a depthfilter, or a depth estimator.
 15. A method for determining a measure fora distortion change of a first view synthesized from a second view,caused by a modification of a depth map of the second view from a firststate to a second state, the method comprising starting from a currentsynthesis state of the first view corresponding to a synthesis from thesecond view comprising the depth map modified to the second state in analready processed portion of the depth map and comprising the depth mapunmodified at the first state in an yet to be processed portion of thedepth map, computing a possible successor synthesis state correspondingto a synthesis of the first view from the second view comprising thedepth map modified to the second state in an already processed portionplus a currently processed portion and comprising the depth mapunmodified at the first state in the yet to be processed portion withoutthe currently processed portion; determining a distortion change of adistortion of the current synthesis state of the first view relative toan undistorted version of the first view to a distortion of the possiblesuccessor synthesis state of the first view relative to the undistortedversion of the first view.
 16. A non-transitory computer readable mediumincluding a computer program comprising a program code for performing,when running on a computer, a method according to claim 15.